Quantized hyperalgebras of rank 1
| dc.creator | Chin, William | |
| dc.creator | Krop, Leonid | |
| dc.date | 2004-03-08 | |
| dc.date.accessioned | 2026-07-07T05:06:13Z | |
| dc.date.available | 2026-07-07T05:06:13Z | |
| dc.description | We study the algebra $U_ζ$ obtained via Lusztig's `integral' form [Lu 1, 2] of the generic quantum algebra for the Lie algebra $\frak {g=sl}_2$ modulo the two-sided ideal generated by $K^l-1$. We show that $U_ζ$ is a smash product of the quantum deformation of the restricted universal enveloping algebra $\bold u_ζ$ of $\frak g$ and the ordinary universal enveloping algebra $U$ of $\frak g$, and we compute the primitive (= prime) ideals of $\Uz$. Next we describe a decomposition of $\bold u_ζ$ into the simple $U$- submodules, which leads to an explicit formula for the center and the indecomposable direct summands of $\Uz$. We conclude with a description of the lattice of cofinite ideals of $\Uz$ in terms of a unique set of lattice generators. | |
| dc.identifier | https://arxiv.org/abs/math/0403144 | |
| dc.identifier | http://arxiv.org/abs/math/0403144 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70394 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 17B37 | |
| dc.title | Quantized hyperalgebras of rank 1 | |
| dc.type | text |